Exercise 2.8

Answers

(a): If $H$ is closed under linear combination, for any $x$ , $ḡ (x)$ is weighted (by probability of data) average of hypotheses in $H$ , so $ḡ (x) \in H$ .
(b): If $H$ is a set of functions defined on intervals, e.g. $f (x) = c$ when $x \in [a, b]$ , otherwise $f (x) = 0$ . Then $ḡ (x)$ probably won’t have constant value in an interval and not in the original hypothesis set.
(c): For binary classification, each $g (x)$ will have value $+ 1$ or $- 1$ , when weighted by probabilities, the average is not binary anymore.

niuers

2021-12-07 22:10